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Each of the following vectors is given in terms of its x and y components. Find the magnitude of each vector and the angle it makes with respect to the +x axis.

Ax​=5,Ay​=0.

1 Answer

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Final answer:

To calculate the magnitude of the vector with components Ax=5, Ay=0, we use the Pythagorean theorem, resulting in a magnitude of 5. The angle with respect to the +x axis is determined by the arctangent of Ay/Ax, which is 0 degrees in this case, indicating that the vector lies along the +x axis.

Step-by-step explanation:

To find the magnitude and angle of a vector given its x and y components (Ax and Ay), we make use of trigonometric functions and the Pythagorean theorem. For the vector with components Ax​=5, Ay​=0, the magnitude (A) can be calculated using the square root of the sum of the squares of the components: A = √(Ax2 + Ay2).

Substituting the values given:




The angle (θ) a vector makes with respect to the +x axis is determined by the formula θ = tan-1(Ay/Ax). As Ay is zero, the angle is θ = tan-1(0/5) which is simply 0 degrees. Therefore, the vector lies along the positive x-axis. In this case, figuring out the direction is straightforward, as the y-component is zero, hence there is no deviation from the x-axis.

User Jonathan Spooner
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